ElectricPavlov

sin x    has midline at 0    this one is shifted up 5

sin x + 5

maximum usually occurs at  pi / 2    this one occurs at  2  so the curve is shifted Right by .4292     (because  2- .4292 = pi / 2)

sin (x -.4292) +5     

the maximum is usually 1       shifted up 5 in our example = 6     but this maiximum is 7 ....this would be 2 shifted up 5

   so amplitude is 2

2 sin (x-.4292) + 5

AREA of the trapezoid ===     2 m  x  (1.4 + .6)/2 =  2 m^2

VOLUME of the pond = Area of trapezoid by width    = 2 m^2 x 1 m = 2 m^3

In 30 minutes volume lost =  .2m x 2 m x 1 m / 30 min  = ..4 m^3 /30 min

2 m^3    /  .4 m^3/ 30 min =   150 minutes to completely drain      

Question is unclear    :  it will take 150 minutes to completely drain from the start    or    120 from the time 20 cm has drained .

Second one..... according to the line segment on the number line ,  x is between -2 and +7   but does not include the actual -2 (hollow dot)

so      x > -2      (or  -2< x)          and  x <=7     combine to form      -2< x <= 7

The first one is A       cover up the  '7' and look at it ....it says   'y' is greater than or equal to 3

                                  now cover up the '3'      it says y is less than 7    

Originally     24   red       24 black

  then           16 red         24 black      ratio  red/black now   16:24 =  2:3

2 x 10¹²  /  5 x 10⁶  =    .4 x 10⁶ =   4 x10⁵  =   4 00,000  times larger

50p q²  + 6p-p

50 p q²  + 5p

5p ( 10q² + 1)   

 I am not sure, but I think the theoretical probability of rolling a 2  is  1 out of 6    1/6    (assuming a fair die)

     your EXPERIMENTAL probability is  4 out of 24   ....  also  1/6

It is flipped     so it is   -x^2

Now look at the value at x = 1     it changes from    y = 1   to   y =  -4

   so the original f(x) is flipped AND multiplied by 4

     and becomes   g(x) = - 4 x^2

https://web2.0calc.com/questions/helpppp_30